I made an obviously jocular reference (note the smiley) to Bayesianism
in discussing the differences between doing history and doing natural
science. Allen took my off-hand remark as an opportunity to lecture us
on the putative glories of Popperian philosophy of science as compared
with Bayesianism (as though either of them hand much relevance to the
practice of historical research). First off, no one is REALLY Bayesian
when it comes to history. I don't think I've ever come across anyone
seriously claiming a specific probability with respect to any historical
event. Even if we were to take my little joke seriously, however, Allen
fails to mention that Popper's falsificationism turns out to be nothing
more or less than a limiting special case of Bayesianism -- viz., when
the probability of the data given the theory is zero (p(D|T)=0). In
other words, when the data flatly contradicts the theory, because p(D|T)
appears as a multiplier in the numerator of the Bayesian function,
whatever the value of the other elements in the Bayesian function --
p(T), p(D) -- the whole thing goes immediately to 0 (i.e., in Popperian
terms, it is falsified).
What makes the Bayesian approach so much more useful and interesting
than Popper's falsificationism, however, is that it also tells us what
to do when the probability of the data given the theory is NOT 0, but
some number between 0 and 1. For instance, what if I have a theory that
says there is an 80% probablility that airplane will fly over my house
at exactly 2:30 pm (or to make it more "ecologically valid," as they
say, that another hurricane will strike New Orleans this summer). The
Popperian approach is stopped dead in its track by such a probabilistic
prediction (while Popper himself unaccountably says that it's utterly
unimportant how such a prediction turns out). Bayesianism, however,
enables one to generate a new probability for my theory based on my
prediction and the outcome of the corresponding observation. As
confirming evidence mounts, the theory's probability rises (and old
Popperians moan). As disconfirming (but not flatly falsifying) evidence
comes in, the theory's probability goes down.
Regards,
--
Christopher D. Green
Department of Psychology
York University
Toronto, ON M3J 1P3
Canada
416-736-5115 ex. 66164
[EMAIL PROTECTED]
http://www.yorku.ca/christo
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